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We study the following open question: If a ring R is the sum of two subrings A and B both satisfying a polynomial identity, does R itself satisfy a polynomial identity? We give a positive answer to this question in case R satisfies a special " mixed " identity or (AB) k ⊆ A for some k ≥ 1 or A or B is a Lie ideal. Our approach is based on a comparative(More)
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